
Journal of Lie Theory 31 (2021), No. 2, 439458 Copyright Heldermann Verlag 2021 Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers Saudamini Nayak Institute of Mathematics and Applications, Bhubaneswar, India anumama.nayak07@gmail.com [Abstractpdf] Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $$ s(L) = \frac{1}{2}[(m + n  1)(m + n 2)]+ n+ 1  \dim \mathcal{M}(L), $$ where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of all nonabelian nilpotent Lie superalgebras with $s(L)=0$ is known from a previous publication of the author [{\em Multipliers of nilpotent Lie superalgebras}, Comm. Algebra 47/2 (2019) 689705]. This paper is devoted to obtain all nilpotent Lie superalgebras $L$ when $s(L) \leq 2$. Further, we apply those results to list all nonabelian nilpotent Lie superalgebras $L$ with $ t(L) \leq 4$. Keywords: Nilpotent Lie superalgebra, multiplier, special Heisenberg Lie superalgebra. MSC: 17B30; 17B05. [ Fulltextpdf (161 KB)] for subscribers only. 